Following is the frequency distribution of life length in hours of 100 electric bulbs :

If the median of life length in 20 hours, then what are the missing frequencies (x, y)?

Options

A. `(28,13)`
B. `(23,18)`
C. `(31,10)`
D. `(25,16)`

Answer

C

Explanation

Let `x=31 and y=10`
`{:(" C.I.","x","f","cf"),("8.5 - 13.5","11","7","7"),("13.5 - 18.5","16","31","38"),("18.5 - 23.5","21","40","78"),("23.5 - 28.5","26","10","88"),("28.5 - 33.5","31","10","98"),("33.5 - 38.5","36","2","100"):}`
`because" "N=100, therefore(N)/(2)=50`
`therefore" Median group is 18.8 - 23.5"`
`therefore" "L_(1)=18.5,L_(2)=23.5, C=38, h=5, f=40`
`((N)/(2)-C)`
`therefore" Median "=L_(1)+(((N)/(2)-C))/(f)xxh`
`=18.5+(50-38)/(40)xx5=18.5+(12xx5)/(40)=18.5+1.5=20`
Thus, our assumption is correct. Therefore missing numbers are 31 and 10 respectively.